Does anyone have information/experience on the correlation between the hosting company and the search engine ranking? I wouldn't think there should be a correlation but some time ago I started a new site with a new hosting company and then completely forgot about it... after a while I discovered it was ranking quite well (for a site that I didn't put any effort into).... it could be the name of the site but I have a feeling it has something to do with the hosting company..
I don't think the hosting company matters. However, the hosting ip might matter if your site shares the same ip with 300 other sites. If their site get into trouble then yours might be affected.
Yea, it matters....Not really, but if your site goes down often or for long periods of time you can get hit pretty badly by SEs. So, technically no they dont care, just make sure your host is reliable....
Perhaps you can purchase a dedicated IP... Most hosting companies offer this feature as an add-on. However, it might cost you an extra $5-$10 per month depending on the company. Just make sure that it's on a separate C class, if at all possible.
If you have a shared hosting with an IP Google has trouble with (spamming, blackhat etc), your site can be affected.
No, from a search engine's perspective, it doesn't even know what host you're using. All it sees is a hostname and an IP address, which as has been stated previously, shouldn't be a big issue one way or the other as long neither has anything bad associated with it.